Weight Painting - Objects Getting Left Behind
Your can choose from a few different options to improve your situation.

Option 01 Copy Vertex weights in Edit Mode  

The correct vertex group for the particular band is selected in the UI from the vertex list in the Mesh Panel, as seen in the image below.  Know the band is distant from Bone and currently not attached to body of glove.  The disconnected band is moved .5 Y axis units for visibility.  The band is selected.  A Single vertex is selected on the perimeter of glove as shown by yellow arrow.  The weights of this single vertex could be cleaned up, not shown here.  The Vertex Copy weights button is clicked. Weights are changed.  Disconnected band is moved -.5 Y axis units. Repeat on other side.  

This will improve the immediate problem and assist your understanding. Improvement is the goal here and a light discussion of weight assignment.  Not 100% physical realism. If I had more time I would examine and clean up the source weights. Hopefully there will be more steps to improve the model outside this question. Currently the glove can intersect and pass through the organic skin portion of the mesh, which is not high physics realism. Answer time is finite.  In the little experiments I did, this gave the best result in some small amount of time.  Of course the whole mesh could be painted by hand and other controls added, with no automatic weights. More realism would come with larger time consumption.

Other problems will remain which may require a new question. 



Copy Vertex Weight Image above.  Note arrow showing single source vertex of the well behaved body of glove.



Option 02. Modify Mesh and Armature Parent again.  Exercise for the OP


Connect the glove band to the the body of the glove. The band is distant from the bone. It is not connected to the body of the glove by vertices.  Vertex connectivity is taken into account for some automatic weights.  Distance to Bone is taken into account.  The details are not discussed here.   Then parent to armature again and test.


There could be an argument to consider the glove as very different than the human skin of the mesh. Some might say the glove is like clothing and should be a separate mesh.



Option 03.  More Weight Paint .. Weight Assignment.

Please paint/inspect again the band of your glove.  Please improve any weight paint results you see below.  2 Options.


Use Weight Paint mode 
Edit Mode.  Select the band only.  Select the named group. Assign a weight of 1.0 which is full weight.


Band is not yet painted.



In the image above.  We see above we see your model.  The body of the glove is painted. The band of the glove has zero weights.  In weight paint mode please paint the band.  See how the correct group is selected before we paint. Well there are possible two correct groups as candidates. 

Weight Painted Band in the Correct group.



Painting of band has begun.  Red color. In edit mode of the mesh I selected the band prior to my weight painting.

The topic of weight painting can be mastered.  This short answer will not be equivalent to a video weight painting tutorial.

Direct assignment to group in edit mode of mesh.



Weight assignment. See the arrow. Image above.



Showing weight in edit mode of mesh.  See arrow. Image above.